A puzzle....

Iliya · Fri 09/04/2010 12:00:35

Three wise men are told to stand in a straight line, one in front of the other. A hat is put on each of their heads. They are told that each of these hats was selected from a group of five hats: two black hats and three white hats. The first man, standing at the front of the line, can't see either of the men behind him or their hats. The second man, in the middle, can see only the first man and his hat. The last man, at the rear, can see both other men and their hats.

None of the men can see the hat on his own head. They are asked to deduce its color. Some time goes by as the wise men ponder the puzzle in silence. Finally the first one, at the front of the line, makes an announcement: "My hat is white."

He is correct. How did he come to this conclusion?

Crimson Wizard · Fri 09/04/2010 12:19:04

Answer:

Spoiler

If 2 first men were both wearing BLACK hats, the 3rd man would say that he is wearing WHITE.
This means, first 2 men are wearing either 2 WHITE hats or BLACK AND WHITE hats.
SO, If first man wears BLACK hat, 2nd man would say that HE is wearing WHITE. But he sais nothing.
That means that first man is wearing WHITE hat in any case.

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NsMn · Fri 09/04/2010 12:51:49

No. Correct answer:

Spoiler

The first man GUESSED.

...

...no, seriously, that's all. He had a 50:50 chance, why shouldn't he?

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Ali · Fri 09/04/2010 12:55:58

Surely it's a 60:40 chance, NsMn.

The REAL correct answer is:

Spoiler

The white hat was the wise man's Mother.

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Stupot · Fri 09/04/2010 12:59:55

Either:

Spoiler

He saw his reflection in a shop window...

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Or:

Spoiler

He doesn't know the colour of the hat he has been made to wear for this exercise, but is simply stating a fact about a hat which he does happen to own...

"My hat is white (but its at home on the hatstand)"

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or

Spoiler

The guy behind him passed him a piece of paper saying "your hat is white".

[close]

Calin Leafshade · Fri 09/04/2010 13:06:32

Spoiler

He's a Klu Klux Klansman and would be seriously pissed if his hat was not white

[close]

Anian · Fri 09/04/2010 13:16:16

Spoiler

obviously telepath

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Crimson Wizard · Fri 09/04/2010 13:27:19

You, guys, are no fun at all. I spent my brain energies and 15 minutes of my life to solve a puzzle. You are wasting your fingers to type a nonsense. Shame on you 8)

Stupot · Fri 09/04/2010 13:35:12

Most of my favorite riddles have silly solutions similar to the one's I posted. I'm sure this one has a more mathematically logical answer, but I can't work it out, So I'm going the silly route. I can't get your answer to make sense either, Crim.

Ali · Fri 09/04/2010 13:37:40

I feel bad, I've never been accused of wasting my fingers before. I did solve the puzzle before typing some nonsense.

Now the puzzle is solved we need another, or it's nonsense from here on in.

OneDollar · Fri 09/04/2010 13:52:14

Quote from: Stupot on Fri 09/04/2010 13:35:12
I can't get your answer to make sense either, Crim.

He's right.

Spoiler

Both the first and second guys know that the third guy will speak up if they are both wearing black hats (because if they are both wearing black hats there are no black hats left so the third guy will know he's wearing a white one). When he doesn't speak both the first and second guy realise that one of them is definitely wearing a white hat and the other is wearing either a white or a black hat. Because the second guy knows this he also knows that if he can see the first guy wearing a black hat, then his hat must be white. When he doesn't speak up either the first guy concludes that this isn't the case and so his hat must be white.

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Quote from: Ali on Fri 09/04/2010 13:37:40
Now the puzzle is solved we need another, or it's nonsense from here on in.

Yes, more riddles! Can't think of a good one offhand though.

Iliya · Fri 09/04/2010 13:56:17

And now the scores:

Crimson Wizard - A
OneDollar - B
Ali - Я
Stupot - Я
anian - Я
Calin Leafshade - Я
NsMn - Я

OneDollar · Fri 09/04/2010 14:18:21

Hah, I didn't solve it I just rewrote Crimson's answer

. I've seen the puzzle before though.

OK, Googling brings up this one:

There are an even number of coins on a table, and there are the same number of coins with heads up as tails up. Your task is to separate the coins into two piles, where the number of heads up in each pile is equal. The problem is you are blindfolded and can't tell which way up each coin is facing. How do you do it?

tzachs · Fri 09/04/2010 14:22:52

Quote from: OneDollar on Fri 09/04/2010 13:52:14
Yes, more riddles! Can't think of a good one offhand though.

Ok, if you insist:

100 men are being kept captive by a big, bad, ugly witch. The witch tells them: "Tomorrow I'm gonna put you in a straight line, one in front of the other, where each one will see all of the guys in front of him and not the guys before him. I will put a hat on each of you, it will be either black or white, with no other limitations (it can be 50/50 or 100/0, everything goes). Each man, from the last in the line (the guy who sees all the rest) until the first one (the guy who sees no one) will have to guess the color of his hat, if he succeeds, he lives, if he fails, he dies."

The 100 guys have all night to plan together their tactics. What do they need to do in order to rescue the most guys possible (and what is the most guys possible to be rescued)?

NsMn · Fri 09/04/2010 14:33:44

Since I can only solve monkey's riddle by cheating (I can feel if a coin is face up or not, pfah!

), I can only post these old ones:

1. A man has 17 camels. As he's close to death, he speaks to his three sons: "Mustafa, you shall inherit half of my camels. You, Babar [heh], shall receive one third of my camels, and Amir, I give you 1/9 of them.".
So it happens that the old man dies, and the sons are in a dilemma: They can't part them up without killing one camel. What should they do? Well, coincidentally, as they sit out on the street and discuss, a wise man in a luxurious wagon driven by a camel comes by and hears them fighting over their heritage. He decides to help the three brothers.

Question: What will the wise man do?

2. After the man died, he rises up to the heavens and finds himself in front of two doors - one of them leads to heaven, the other one to hell...
...wait. forget about that riddle. The solution doesn't even work.

Stupot · Fri 09/04/2010 14:39:04

@OneDollar

Spoiler

do the two pile's have to make use of all the coins, or could you just take two of the coins and put them into 2 piles of 1, as long as one is a head and one is a tail?

[EDIT] Infact... that's my answer.. there are only two coins, and if you've already been told that their are an equal number of heads and tails then you know you just need to put them into two piles of one...

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@tzachs - I wont answer this because I found it when I was trying to find the answer to the first riddle.

Calin Leafshade · Fri 09/04/2010 14:40:28

tzachs: If the first person simply repeats the colour of the hat in front then the person in front will know what colour their hat is.. thus saving at least 99 of the 100 and gives the last one a 50 50 chance.

Ali · Fri 09/04/2010 14:52:42

Quote from: NsMn on Fri 09/04/2010 14:33:44
1. A man has 17 camels. As he's close to death, he speaks to his three sons: "Mustafa, you shall inherit half of my camels. You, Babar [heh], shall receive one third of my camels, and Amir, I give you 1/9 of them.".
So it happens that the old man dies, and the sons are in a dilemma: They can't part them up without killing one camel. What should they do? Well, coincidentally, as they sit out on the street and discuss, a wise man in a luxurious wagon driven by a camel comes by and hears them fighting over their heritage. He decides to help the three brothers.

Question: What will the wise man do?

Um...this seems a bit too obvious to be the answer:

Spoiler

Loans them his camel, so they have 18. Gives 9 to Mustafa (1/2), 6 to Babar (1/3) and 2 to Amir. Then he takes the remaining camel and rides off into the sunset...?

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Crimson Wizard · Fri 09/04/2010 15:03:33

Quote from: NsMn on Fri 09/04/2010 14:33:44
1. A man has 17 camels. As he's close to death, he speaks to his three sons: "Mustafa, you shall inherit half of my camels. You, Babar [heh], shall receive one third of my camels, and Amir, I give you 1/9 of them.".
So it happens that the old man dies, and the sons are in a dilemma: They can't part them up without killing one camel. What should they do? Well, coincidentally, as they sit out on the street and discuss, a wise man in a luxurious wagon driven by a camel comes by and hears them fighting over their heritage. He decides to help the three brothers.

Question: What will the wise man do?

Okay, lemme guess...

Spoiler

He added his own camel to their 17, thus having 18 in summ. He then divided those 18 as their father required (half = 9, third = 6, ninth = 2, total 17, and returned his own camel back.

[close]

By the way, I must say that

Spoiler

this puzzle actually remind me of a programmer's integer division problem

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Crimson Wizard · Fri 09/04/2010 15:05:48

Quote from: Calin Leafshade on Fri 09/04/2010 14:40:28
tzachs: If the first person simply repeats the colour of the hat in front then the person in front will know what colour their hat is.. thus saving at least 99 of the 100 and gives the last one a 50 50 chance.

Calin, you're completely wrong. If the person repeats the colour of the NEXT guy, he will save himself only if he has SAME colour. Thus 99 of the 100 is not the LEAST saved, but MOST possible saved. Least saved is actually 1, the first in the line (one who does not have anyone in front).